The generator matrix

 1  0  0  1  1  1  X  X  1  1  1 X^2 X^2 X^2+X  0  1  1  1  X  1 X^2+X  1  X  0  1  1  1  1  X
 0  1  0  0  1  1  1  1 X+1  X X^2+X+1  1  X  1  1  X X^2+X+1 X^2+X+1 X^2+X  X X^2+X  1  1  1  0 X^2+1 X^2+X X^2+X X^2
 0  0  1 X+1 X^2+X+1  0  1  X X^2+X+1  1  X  1  1 X+1 X^2+X  X X^2+1 X^2+X+1  1 X^2+X+1  1 X^2 X^2+X+1  0  1  X X^2+X  X  X
 0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+243x^24+112x^25+484x^26+272x^27+814x^28+288x^29+844x^30+224x^31+439x^32+112x^33+204x^34+16x^35+34x^36+4x^38+5x^40

The gray image is a linear code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.16 in 0.246 seconds.